(II-30 1). Consider the game with matrix

(a) Note that this game has a saddle point.

(b) Show that the inverse of the matrix exists.

(c) Show that II has an optimal strategy giving positive weight to each of his

columns.

(d) Why then, don't equations (16) give an optimal strategy for II?

Consider the diagonal matrix game with matrix (18).

(a) Suppose one of the diagonal terms is zero. What is the value of the game?

(b) Suppose one of the diagonal terms is positive and another is negative. What

is the value of the game?

(c) Suppose all diagonal terms are negative. What is the value of the game?

Player II chooses a number j 2 f1; 2; :::; ng and I tries to

guess what it is. If he guesses correctly, he wins 1. If he guesses too high, he

loses 1. If he guesses too low, there is no payo. Set up the matrix and solve.